17/08/2024
The 7.5m roof load width (RLW) is defined measured parallel to the roof surface. This is generally inconvenient. Most handbooks of frame formula define uniformly distributed loads (UDL), distributed either horizontally or vertically, and this is because it is also easier to derive formula this way, it is also beneficial to look at the influence of a load in the horizontal and vertical directions. Our codes also define live loads distributed along the horizontal, 0.25kPa roof live load for example is distributed along the projected horizontal dimension not the actual length.
If we have stick of wood with a mass of say 5.94kg/m and it is 6m long, then its total mass is 35.64kg, and this acts through the centre of mass which is 3m from each end. The timber framing code limits roof pitch to 35 degrees, so if we rotate this stick of wood, through 35 degrees, it will still have a mass of 35.64kg acting vertically.
Now if we have rafters at 1.2m centres then the 0.25kPa will produce 0.30kN/m on each rafter. But this is not distributed along the length of the rafter, its distributed along the projected horizontal. It therefore cannot be combined with the deadload of the roof or self weight of the stick of wood, as they are based on different lengths.
The length of the horizontal is x = r.Cosθ = 6*cos(35)=4.915m and the vertical rise is y = 6*Sin(35) =3.441m. So the total live load (LL) is 4.915*0.3=1.47 kN not 6*0.3=1.8kN. So if we want to use the horizontal dimensions the self weight needs to be increased, so that when multiplied by 4.915 it gives the correct total weight. So we could calculate the total weight and distribute along the desired length. So have original length L, and new length x=L.Cosθ , so W=w.L=w1.x, therefore w/w1=x/L=Cosθ, and so w1=w/Cosθ, so the 5.94kg/m becomes 5.94/cos(35)=7.25kg/m distributed along the horizontal. Check: 7.25*4.915 = 35.63kg, which if remove some of the rounding error is acceptable.
Similarly don't want to work with 40 kg/sq.m or 0.4kPa distributed along length of rafter, want to work with horizontal distances between walls, not dimensions along roof slopes. So allowing for 35 degree roof pitch the load becomes 0.4/cos(35)=0.49kPa distributed along the horizontal, or 49 kg/sq.m. But now also working with horizonal distances so the 7.5m RLW, now becomes a load width of 6.144m on the horizontal.
Our flat verandah roof probably only a weight of 0.2kPa, with pitch less than 10 degrees. So converts to 0.2/cos(10)=0.20kPa so no real change.
So crudely the maximum load permitted along the wall is 6.144*0.49 = 3.01kN/m, which should match 7.5*0.4=3.00kN/m.
Typically the load width to a wall is half the distance between parallel walls, or half the width of the house. It could be more or less depending on how the structure is configured. But if symmetrical gable roof spanning between external walls, its half the width of the building at that point. So our building can have a maximum width of 2*6.144=12.29m, so if that is what we are starting with then we have no reserve for attaching a verandah.
So assume house has 2 rooms 3.6m wide and a 1.2m hallway between, so width is 2*3.6+1.2=8.4m, so load width to wall is 8.4/2=4.2m. Maximum permitted is 6.144m, so we have some reserve: 6.144-4.2=1.94m, which is certainly not the 6m or more people want to sling of their house roof and walls. But the verandah roof is only about 0.1 to 0.2 kPa roof weight. Where as our limit is based on 0.4 kPa (or 0.49kPa on horizontal).
So 4.2*0.49=2.06kN/m, and limit is 3kN/m, so 3-2.06=0.94kN/m. So canopy weight is 0.2kPa, and so s=w/p=0.94/0.2=4.7m. Check: 4.7*0.2=0.94kN/m
Now given that this is the load width of the canopy on the house wall, the canopy width can be twice this so 4.7*2 = 9.40m.
However, this is only considering one of many load cases concerned with the design of the house/veranda combination. Also need to consider live loading requirements, and wind loading. So would consider load combinations such as 1.2DL+1.5LL, and 0.9DL+WL. We also making an assessment on a defined RLW, and we don't know which load case is critical to determining such load width. Just making an assumption that the load is proportional to the weight, that everything else is constant and varies in similar manner.
All that basically done is determine that the weight of the verandah is not likely a critical issue if it uses lighter weight construction to the house. However the wind uplift will be critical, as will the resistance of the installed house connections.
So for wind class N1, qzu=0.69kPa, adopt Cpn=1.1, so pn=Cpn.qzu= 1.1*0.69=0.76kPa, and vertical, uplift component of wind for the RLW=7.5m, is LW=6.144m, so w=0.76*6.144=4.67kN/m, which is greater than the maximum 3kN/m of roof weight permitted, therefore there will be uplift at the roof and tie-down required.
But house likely designed for the 4.2m load width only not the maximum, so for w=0.76*4.2=3.19kN/m , and roof weight was only 2.06kN/m, so net uplift of 3.19-2.06=1.13kN/m, and from previous post the wall weight is less than this, so the weight of the concrete footing is important.
Longitudinal wind pressures on canopies vary between about 0.3 and 0.4, so even if transverse gets down to 0.2 such is not relevant. For narrow canopies the pressure coefficient can be around 1 to 1.5, which is slightly less than the eaves overhang at 1.6. But if we have a steep pitch and block the volume under then the coefficient can get still higher. A blocked volume is something like a large caravan parked under a carport: it is not a side wall or fence.
So house tie-down designed for 1.13kN/m, so assuming a nail in the footing is worth 1kN, and placed at every wall stud at 600mm centres, then it provides 1.67kN/m tie-down, but at 1.2m centres, it only provides 0.83kN/m resistance. Check: 1.13*1.2=1.36kN required at every wall stud carrying a rafter. An anchor bolt can likely provide at least 5kN at each wall stud, so 5/1.2=4.17kN/m. We thus have reserve capacity at the bottom plate. But not necessarily have adequate resistance between wall stud and bottom plate to provide reserve to attach a verandah.
So reserve capacity in house roof and wall tie-down connections needs to be checked before deciding on size of attached verandah. The bottom plate to slab connection, and wall stud to bottom plate connections are not readily accessible and therefore impractical to strengthen. It is therefore preferable to strengthen these connections when designing the house in the first instance.
The timber framing code limits tension in a wall stud to 8.5kN, but there a few timber framing connections which develop this capacity in the wall stud. The nominal, traditional connections, have less than 1kN capacity, and close enough to zero to be considered zero and none existent. Some codes require minimum connection capacity to be at least 50% of member capacity. So minimum connection would be 8.5/2=4.25kN, which would require use of framing brackets or steel strap to all connections not just nailing. For JD4, steel strap with 2 nails would give 3.5kN for wall stud to plate connection, whilst 3 nails would push up to 4.7kN capacity. whilst two nails through the plate into stud is worth only 0.17kN, and relatively useless.
Thus changing roof cladding from concrete roof tiles at 54.6kg/m² to steel roof cladding at 5kg/m² is going to make a big difference to the tie-down requirements in the house roof and wall framing. Its is not just a visual or decorative change. Similarly slinging an extra few metres of verandah roof from a house roof/wall structure is going to increase uplift on the house structure. The house connections likely don't have adequate reserve capacity, and therefore the verandah should be freestanding, unless want to consider the verandah a proper house renovation and strengthen the house wall structure. Which requires removing the internal lining from the wall frames, or removing bricks and creating openings from the outside to access the bottom plates.
Main issue here however is that we can convert our loads from working along the true length of the roof slope, to working on the projected horizontal length. Our live loads and wind uplift loads are on the horizontal, but our dead loads and self weights are along the true length of the element. Roof wind load also has a horizontal component, distributed on projected vertical height, which can be considered separately. Working with these horizontal distances can make some calculations easier. Our primary concern is maximum width of canopy can put on house wall.
Though should be careful with the loads. Whilst the standardised loads of 0.1 to 0.2kPa are along the slope of the roof, the 0.4kPa of the roof on the wall is already likely in a horizontal plane. So I'm not certain why AS1684 uses RLW aligned with slope to size wall framing.
Will take a closer look at that. But note ceiling is in horizontal plane, and roof structure sloping. So one part needs converting and the other doesn't.